Enter your answer and show all the steps that you use to solve this problem in the space provided.
Write the steps in solving -5x + 3 (x + 2)=20
Justify each step with an appropriate property
Step 1: Distribute the 3 to the terms inside the parentheses:
-5x + 3x + 6 = 20
Step 2: Combine like terms:
-2x + 6 = 20
Step 3: Subtract 6 from both sides to isolate the variable term:
-2x = 14
Step 4: Divide both sides by -2 to solve for x:
x = -7
Justification for Step 1: This step follows the distributive property, which states that when multiplying a number by a sum inside parentheses, you can distribute the multiplication to each term inside the parentheses.
Justification for Step 2: This step combines the like terms -5x and 3x, which means adding or subtracting their coefficients. In this case, -5x + 3x simplifies to -2x.
Justification for Step 3: This step subtracts the constant term 6 from both sides of the equation. This maintains equality since any operation performed on one side of an equation must also be performed on the other side.
Justification for Step 4: This step divides both sides by the coefficient -2 to solve for x. Division is the inverse operation of multiplication, so dividing both sides by -2 isolates x. The division maintains equality since any operation performed on one side of an equation must also be performed on the other side.